Abstracts

Parameter identification in dynamical systems using asymptotic observers

Vishal Vasan,  International Centre for Theoretical Sciences, Bangalore

The qualitative aspects of dynamical systems can depend on the parameters of the system and many important questions on the application side involve knowing these parameters. However the observations available to us may only specify a part of the state-vector and hence the initial condition is also an unknown parameter. In this talk, I will introduce a new approach to parameter identification from partial-observations of a dynamical system using asymptotic observers. The main contribution is the definition of a cost function whose minimum is the true parameter. I will present numerical experiments to validate the approach and show that our approach behaves stably even in the presence of errors (either observational noise and/or model specification error). In the context of ordinary differential equations (linear and nonlinear) with finite-dimensional parameter-space, we have a good theoretical understanding of why the method works. I will end with a discussion on how these ideas can be ported over to partial differential equations, particularly those arising in the context of water-waves.